A326881 Number of set-systems with {} that are closed under intersection and cover n vertices.

1, 1, 5, 71, 4223, 2725521, 151914530499, 28175294344381108057

Offset

0,3

Links

Table of n, a(n) for n=0..7.

Formula

Inverse binomial transform of A102895. - Andrew Howroyd, Aug 10 2019

Example

The a(2) = 5 set-systems:
  {{},{1,2}}
  {{},{1},{2}}
  {{},{1},{1,2}}
  {{},{2},{1,2}}
  {{},{1},{2},{1,2}}

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n]]], MemberQ[#, {}]&&Union@@#==Range[n]&&SubsetQ[#, Intersection@@@Tuples[#, 2]]&]], {n, 0, 3}]

Crossrefs

The case also closed under union is A000798.

The connected case (i.e., with maximum) is A102894.

The same for union instead of intersection is (also) A102894.

The non-covering case is A102895.

The BII-numbers of these set-systems (without the empty set) are A326880.

The unlabeled case is A326883.

Cf. A003465, A014466, A102896, A102897, A193674, A193675, A306445, A307249, A326878.

Sequence in context: A193436 A193501 A133990 * A120808 A092204 A079874

Adjacent sequences: A326878 A326879 A326880 * A326882 A326883 A326884

Keyword

nonn,more

Author

Gus Wiseman, Jul 30 2019

Extensions

a(5)-a(7) from Andrew Howroyd, Aug 10 2019

Status

approved